I believe that Satan (and his fellow demons) are not omniscient, therefore whenever someone senses their presence, one should speak aloud, “Jesus”, and they will flee. Yet how does Satan influence, and play upon, our unspoken thoughts and insecurities? Is he insinuating the negative thoughts into our heads?
The starting viewpoint you mentioned is a false and unbiblical notion of Satan and his army of demons. The Bible does not teach that the enemy will flee merely at the uttering of the name “Jesus.” On the contrary, the Bible teaches that such notions are merely superstition and likely to plunge the believer into serious trouble:
Acts 19:13 But also some of the Jewish exorcists, who went from place to place, attempted to name over those who had the evil spirits the name of the Lord Jesus, saying, “I adjure you by Jesus whom Paul preaches.”
Acts 19:14 Seven sons of one Sceva, a Jewish chief priest, were doing this.
Acts 19:15 And the evil spirit answered and said to them, “I recognize Jesus, and I know about Paul, but who are you?”
Acts 19:16 And the man, in whom was the evil spirit, leaped on them and subdued all of them and overpowered them, so that they fled out of that house naked and wounded.
Notice the mention of the name Jesus did nothing to stop these demons from harming the seven brothers. From this passage we see conclusively that Jesus’ earthly name is not a magic word that compels the demon realm to flee. Demons are far more powerful than us, and therefore only God’s power is capable of defeating them.
For more information on the correct biblical view of such things, please see: